In this paper, the 331 model \(SU_{c}(3) \times SU_{L}(3) \times U(1)_{X}\)  is studied with RHNs and added to a discrete symmetry \(\mathbb {Z}_{2}\) .
The model includes an enlarge fermion sector with three new exotic quarks and one conjugate left-handed neutrino in the multiplets of leptons.
The Higgs sector is extended to contain three scalar multiplets whose the vacuum expected values (VEVs) scales yield masses for all particle content via spontaneous symmetry breaking (SSB). The mechanism is similar to the two-Higgs doublets models (2HDs). The model includes new heavy gauge bosons in which the LHC constraints their masses at the TeV scale. In the basis of the physical fields, the couplings of the exotic quarks with the charged gauge boson are investigated whose phases imply into extra CP violation. The couplings of the physical scalar fields with \(Z^{\prime }\)  are obtained in the Higgs sector. The discrete symmetry \({\mathbb {Z}}_{2}\)  guarantees the stability of physical scalar fields in which it is the candidate to the DM content of the 331 model. The DM relic density is calculated as function of the DM scalar mass at the TeV scale for the process DM-anti-DM scalar annihilated into SM fermion-anti-fermion pairs through the \(Z^{\prime }\)  portal. The parameter space of DM mass versus the \(Z^{\prime }\)  mass is obtained reproducing
the observed relic density and including the bounds of PANDAX2017 [1]}, XENON1T(2t.y) [2]} and LUX [3]} experiments.
